Petros Valettas

Assistant Professor

Contant Information

University of Missouri

Mathematics Department

303 Mathematical Sciences Building

Columbia, MO 65211

E-mail: valettasp@missouri.edu

Research Interests

Asymptotic Convex Geometry

Geometric Functional Analysis

High-Dimensional Probability

Probabilistic Methods in Analysis and Geometry

Teaching

  • Current Teaching at MU.

    • CMP_SC 7001/MATH 7960: Probability and Computing (Spring 2022)

    • MATH 1700: Calculus II (Spring 2022)

  • Past Teaching at MU.

    • CMP_SC 8001/MATH 8202: High-Dimensional Probability (Fall 2020)

    • CMP_SC 7001/MATH 7960: Probability and Computing (Fall 2019, Spring 2021)

    • MATH 4700/7700: Advanced Calculus I (Fall 2019, Spring 2021)

    • MATH 4140/7140: Matrix Theory (Summer 2018)

    • MATH 4100/7100: Differential Equations (Spring 2018)

    • MATH 2320: Discrete Mathematical Structures (Spring 2019, Fall 2019, 2020)

    • MATH 2300H: Calculus III (Fall 2021)

  • Past Teaching at Texas A&M.

    • Mathematical Probability

    • Topics in Applied Mathematics

    • Linear Algebra

    • Calculus I and III

  • Lecture Notes.

    • Real Analysis: Metric Spaces, University of Athens (2009). pdf

Publications and Preprints

  • On the existence of subgaussian directions for log-concave measures (with A. Giannopoulos and G. Paouris), Contemporary Mathematics 545 (2011), 103-122.

  • Psi(α)-estimates for marginals of log-concave probability measures (with A. Giannopoulos and G. Paouris), Proceedings of the American Mathematical Society 140, no. 4 (2012), 1297-1308.

  • On the distribution of Psi(2)-norm of linear functionals on isotropic convex bodies (with A. Giannopoulos and G. Paouris), Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics 2050 (2012), 227-253.

  • Distances between classical positions of centrally symmetric convex bodies (with E. Markessinis), Houston Journal of Mathematics 41 (2015), 187-211.

  • On the geometry of log-concave probability measures with bounded log-Sobolev constant (with P. Stavrakakis), Proceedings of the Asymptotic Geometric Analysis Programme, Fields Institute Communications 68 (2013), 359-380.

  • Neighborhoods on the Grassmannian of marginals with bounded isotropic constant (with G. Paouris), Journal of Functional Analysis 267 (2014), 3427-3443.

  • Random version of Dvoretzky’s theorem in ell_p^n (with G. Paouris and J. Zinn), Stochastic Processes and their Applications 127, Issue 10 (2017), 3187-3227.

  • On Dvoretzky’s theorem for subspaces of L_p (with G. Paouris), Journal of Functional Analysis 275, Issue 8 (2018), 2225-2252.

  • Inequalities for the surface area of projections of convex bodies (with A. Giannopoulos and A. Koldobsky), Canadian Journal of Mathematics 70 (2018), 804-823.

  • A Gaussian small deviation inequality for convex functions (with G. Paouris), Annals of Probability 46, no. 3 (2018), 1441-1454.

  • On a quantitative reversal of Alexandrov’s inequality (with G. Paouris and P. Pivovarov), Transactions of the American Mathematical Society 371, no. 5, (2019), 3309-3324.

  • Variance estimates and almost Euclidean structure (with G. Paouris), Advances in Geometry 19, Issue 2, (2019), 165-189.

  • On the tightness of Gaussian concentration for convex functions, Journal d' Analyse Mathématique 139, Issue 1 (2019), 341-367.

  • Dichotomies, structure, and concentration in normed spaces (with G. Paouris), Advances in Mathematics 332 (2018), 438-464.

  • Gaussian convex bodies: a non-asymptotic approach (with G. Paouris and P. Pivovarov), Zapiski Nauchnych Seminarov POMI 457 (2017), 286-316.

  • Hypercontractivity and lower deviation estimates in normed spaces (with G. Paouris and K. Tikhomirov), Annals of Probability (to appear).

  • Concentration estimates for functions of finite high-dimensional random arrays (with P. Dodos and K. Tyros), Preprint.

  • Decompositions of finite high-dimensional random arrays (with P. Dodos and K. Tyros), Preprint.

Book

  • Geometry of isotropic convex bodies (with S. Brazitikos, A. Giannopoulos and B-H. Vritsiou) Mathematical Surveys and Monographs 196, Amer. Math. Soc. (2014) AMS